Lemma 3.1 ([1]}) 
Let \(X\)  and \(Y\)  be quasi-projective integral varieties over \(k\)  and let \(\pi \colon Y \rightarrow X\)  be a finite surjective morphism. Let \(k^{\prime }/k\) 
be a finite field extension and let \(T \subseteq Y(k^{\prime })\)  be a set such that \(\pi (T) \subseteq X(k)\) .
If \(\deg \pi > 1\) , then there exist
quasi-projective integral varieties \(Y_1,\ldots ,Y_n\)  over \(k\)  and
finite surjective morphisms \((\pi _i \colon Y_i \rightarrow X)_{i=1}^n\) 
with \(\deg \pi _i > 1\)  such that \(\pi (T ) \subseteq \bigcup _i \pi _i(Y_i(k))\) .

